Relatório de pesquisa 16/09

Reversal Symmetries for Planar Vector Fields, A. Algaba, C. García and M. A. Teixeira, submitted June 02, 2009. AbstractIn this paper, we formulate a comprehensive study of
relevant properties of reversible vector fields. As a consequence, we
prove that the reversibility of the first non-zero quasi-homogeneous
term, respect to some types, of a vector field is a necessary condition
for the reversibility of the vector field. We also provide a
straightforward characterization of the reversibility for
quasi-homogeneous vector fields. Finally, as an application of our
previous results, we analyze some special polynomial and nilpotent
systems, including examples which are centers and non-reversible.